ABSTRACT
This chapter considers some of the more formal aspects of perturbation expansions. The rate at which functions approach limit values is described by comparison with reference functions. The chapter provides order symbols to allow the limiting behavior to be expressed concisely. It explores the behavior of asymptotic expansions. The chapter also discusses the occurrence of nonuniformities in expansions, and identifies the common sources of nonuniformities. Order symbols obey the usual rules of multiplication and division. The order symbol is used to indicate that a function is smaller than a gauge function in the sense that it either tends to zero faster or to infinity slower than the gauge function. Exponential functions tend to zero or infinity faster than powers while the logarithm is slower to approach infinity than powers. The chapter concludes with a review of some of the sources of nonuniformities in perturbation expansions.
